Expected frequencies of codon use as a function of mutation rates and codon fitnesses

A method is shown to determine the expected pattern of codon use for any given set of mutation rates between nucleotides and any set of fitnesses for the codons. If it is assumed that mutations to stop codons are lethal then those codons which can mutate in one step to a stop codon tend to be used less frequently. This tendency is however, a very small one and is not likely to be observable within a single gene. Nor is it necessarily a general tendency. For example, the leucine pretermination codons may be used preferentially when mutations to proline are deleterious. It is shown that different mutation rates (eg: transitions occurring more frequently than transversions) may have as large an effect on codon usage as would strong selection for particular codons. For the model presented, an increase in the rate of transitions strongly decreases the expected frequency of UGG and CRR codons. Other codes are moderately affected by such a change in the mutation rates. Many other models can be examined using this method.